Evaluate each of the following: sin^-1(sin π/6 )

Question

Evaluate each of the following:

\(sin^{-1}(sin\frac{\pi}6)\)

Answer 1

The value of sin\(\frac{\pi}6\) is \(\frac 12\)

∴ The question becomes sin^–1\((\frac 12)\)

The range of principal value of sin^–1 is \([\frac{-\pi}2,\frac{\pi}2] \) and sin\((\frac{π}6)\) = \(\frac 12\)

Therefore, the value of sin^–1(sin\(\frac{\pi}6\)) is \(\frac{\pi}6.\)

sin^–1(sin x) = x

Provided x ∈ \([\frac{-\pi}2,\frac{\pi}2] \)

∴ we can write sin^–1(sin\(\frac{\pi}6\)) = \(\frac{\pi}6\)